In Linear Algebra, when doing the Row Reduction Method to get to an identity mat

Question

In Linear Algebra, when doing the Row Reduction Method to get to an identity matrix, or Echelon Form. Is there one specific way you need to follow in order to get it to the reduced form. Like do I have to get all my 1's first in a diagonal and then all my 0's around it? Do I have to get my 3rd Row cleared up before my 1st row..

I find that I go down columns to get to my row reduced form but my answers are different and I don't know what I'm doing wrong!

I know the principles to be followed:

1. Multiply a row by a non-zero constant.

2. Add one row to another.

3. Interchange between rows

4. Add a multiple of one row to another.

I just don't know if the order of what I make a 1 or 0 first affects my answer. Help please!!

Explanation / Answer

For reduced row echelon form,

firstly make all the first column elements to zero except first row element using the first row.

Next, make all the second column elements to zero except second row element using the second row.

Then, make all the third column elements to zero except third row element using the third row.

We need to go on like this.

This leads to a diagonal matrix.

After getting this, divide every row with the respective diagonal element to get identity matrix.

Thus, we get the reduced row echelon form.

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